The third-ranked Spaniard said on Thursday he has not fully recovered from the upper leg ailment that bothered him during the Barcelona Open final last Sunday. He also said he has a left leg injury.
His first appearance at the Caja Magica in Madrid was scheduled for Saturday.
Alcaraz is a two-time champion in Madrid, having won in 2022 and 2023. He was the second seed this week and in the same half of the draw as Novak Djokovic.
Alcaraz said he did "everything possible to play" but had to make the "tough decision" to withdraw after listening to his body and talking to doctors.
"Madrid is one of the special tournaments for me, it's a tournament that I enjoy, I get to play in front of my fans, it's one of the first tournaments I attended when I was a kid," Alcaraz said.
"A grand slam is a grand slam. If I play here, I could make the injuries worse and stop for several months and that's not worth it."
He said he felt "secure" about recovering in time to play next month at Roland Garros. He won the French Open final last year against Alexander Zverev, who has just leapfrogged the Spaniard to No. 2 in the world after winning in Munich last week.
Alcaraz said he will also try to play in Rome ahead of the French Open, but wasn't 100 per cent sure if he would be able to make it.
Alcaraz needed treatment on his leg during his straight-set loss to Holger Rune in the Barcelona final. He had not practiced in Madrid yet, and said this week that he felt "fine" but was waiting on medical test results to determine whether he would play.
The four-time Grand Slam champion has a 24-5 record this year. In addition to Monte Carlo, he also won in Rotterdam on hard court in February.
